it wasn't social comment or ethnic balance in the driving seat (or captains chair?)

Yes it was, per Roddenberry himself. He intended for the show to attack heated and divisive social policies. In a time when Russia and Asia were the enemy, you had a Russian and an Asian on the bridge. When segregation was rampant, you had a black WOMAN on the bridge. The original series tackled racial and social issues of it's time. Missions included Nazis, Communists, Socialists and many others. Kirk and Uhura shared the FIRST on screen interracial kiss.

For the most part it seems whenever the ship was to go into battle Will Riker will somehow be on command and Picard is stuck on an away mission, or abducted.

My recollection is that Picard was usually in overall command but Riker was oftentimes the one that was responsible for issuing firing orders, course changes, etc. This is actually somewhat realistic for a large warship; the Captain can usually be found in CIC (Combat Information Center) worrying about the "big picture", while the First Officer remains on the bridge and deals with course changes and the like. They don't have a CIC in Star Trek but the overall theory is still valid.

Read this account [usswashington.com] of the USS Washington at Guadalcanal, when she went toe-to-toe with Japanese warships in a surface action. Here's one of the more interesting tidbits:

On Washington's bridge, Lieutenant Ray Hunter still had the conn. He had just heard that South Dakota had gone off the air and had seen Walke and Preston "blow sky high." Dead ahead lay their burning wreckage, while hundreds of men were swimming in the water and Japanese ships were racing in.
Hunter had to do something. The course he took now could decide the war. "Come left," he said, and Washington straightened out on a course parallel to the one on which she was steaming. Washington's rudder change put the burning destroyers between her and the enemy, preventing her from being silhouetted by their fires.

It wasn't the Task Force Commander (Admiral Lee) or even the Washington's Captain ordering course changes, it was the officer who had the Conn, a "mere" Lieutenant in the position of making life-or-death decisions for a warship with a crew of two thousand men.

A ship the size of the Enterprise-D, with a crew of over a thousand, would likely operate in a similar manner. Remember, the Enterprise is a ship, not a fighter jet.

They're armed, they have a system of ranks, they fight the Federation's wars. If that's not a military, what are they? Granted, they do a lot of things that are not in the remit of a traditional military, but as far as I can see, they're still a military.